Chapter 2

RATIONAL NUMBERS

Chapter 1 introduced the concept of rational numbers, real numbers that

can be expressed as a fraction, a terminating decimal, or a repeating deci-

mal. Rational numbers are truly Gestalt, which is to say they are greater

than the sum of their parts. By nature they are merely quotients of integers,

but their complexity requires a unique set of concepts (such as the least

common denominator) and procedures (such as reducing to lowest terms

and transforming rational numbers from fractions to decimals and vice ver-

sa). Through the study of rational numbers, and the careful, often rigorous,

techniques that surround them, unique and otherwise obfuscated proper-

ties of integers are uncovered.

When you divide two integers, you get a fraction. The fancy name

for “fraction” is “rational number,” and that’s what you deal with in

this chapter. Fractions aren’t as hard to handle as most people think—

you just need to know that when fractions are in the mix, you need

to follow specic rules. For instance, you can only add and subtract

fractions if they have the same denominator. Simple enough. However,

if fractions have DIFFERENT denominators, you CAN multiply and

divide them.

Spend some time getting familiar with fractions in this chapter. When

you nish, you’ll be able to change decimals into fractions; change

fractions into decimals; simplify fractions; identify a least common

denominator; and add, subtract, multiply, and divide fractions to your

heart’s content.

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